House Republicans delivered a sharp reality check to the prospect of overhauling the nation's immigration system, with lawmakers declaring Wednesday evening that the House not only rejects the Senate's comprehensive plan passed two weeks ago, but that they will also take a slower, step-by-step approach to tackling the problem.

On the same day that former President George W. Bush implored his fellow Republicans to carry a "benevolent spirit" into the immigration debate, a closed-door meeting of the House GOP revealed deep divisions, particularly on what to do with the 11 million immigrants who are living illegally in the United States.

Securing the border remains their chief priority, but a consensus could also be building around how to address Dreamers - the children of undocumented immigrants.

Rep. Darrell Issa, R-Calif., said Dreamers should be given priority and a vote on a resolution of their status could come late this summer. He added that House Majority Leader Eric Cantor spoke forcefully about the need for allowing Dreamers to be on a path to citizenship.

"We know we have to get it right the first time," Issa said.

While most Republicans agreed Wednesday on the need to reform the nation's immigration laws, some of the House's most conservative members tried to dissuade their colleagues from moving on a path to legalization, which they warned would politically benefit Democrats in the long run.

"Anything that is legalization ends up in citizenship," Rep. Steve King, R-Iowa, said. "If that's the case, I'm opposed to it because it destroys the rule of law."

Rep. Ileana Ros-Lehtinen, R-Fla., quipped that the Republican Party "is like an orchestra," with many members contributing meaningfully to the debate.

"It's not just soloists. We have different points of views," she said. "As we strengthen the borders, which we must, I hope that we can also look at the 11 million who want to legalize their status and contribute in a big way to the greatness of this country because they're patriots too."

Although House leaders indicated there would not be any substantial votes taken during July and likely no major action on the matter until at least September, they pledged not to ignore the issue.

"As a party, we have to face it and have the courage to confront it," Rep. Charles Boustany, R-La., said, echoing the sentiment of many Republicans who believe the party cannot afford to disregard the nation's troubled immigration system.

"There are three categories that those 11 million people go into," Issa, a member of the House Judiciary committee, added. "People that we all agree should remain here. People that we all agree should be removed - criminal aliens, people who have committed crimes, and so on. And then people who may be in between, who may not have the skills to be well-employed here, or whose skills may be suited toward temporary or guest worker programs."

"That's part of why we're doing a comprehensive approach," he said.

The rest of the bill, Issa said, could be taken together or separately, with a priority on border security and enforcement. Regardless, he said Republicans are opposed to a big bill - like the health care reform law signed into law in 2010.